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Article

Tomoeda, Kenji
Behaviour of the support of the solution appearing in some nonlinear diffusion equation with absorption. (English). In: Mikula, Karol (ed.): Proceedings of Equadiff 14. Conference on Differential Equations and Their Applications, Bratislava, July 24-28, 2017. Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing, Bratislava, 2017. pp. 359-368
MSC: 35B99, 35K65, 65M06
Keywords:
Nonlinear diffusion, support dynamics, finite difference scheme
Summary:
Numerical experiments suggest interesting properties in the several fields of fluid dynamics, plasma physics and population dynamics. Among such properties, we may observe the interesting phenomena; that is, the repeated appearance and disappearance phenomena of the region penetrated by the fluid in the flow through a porous media with absorption. The model equation in two dimensional space is written in the form of the initial-boundary value problem for a nonlinear diffusion equation with the effect of absorption. In this paper we show some numerical examples and prove such phenomena.
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